Analysis of X-ray scattering microstructure data for implementation in numerical simulations of ocular biomechanical behaviour

Abstract

This study aimed to analyse microstructure data on the density and orientation of collagen fibrils in whole eye globes and to propose an effective method for the preparation of data for use in numerical simulations of the eye’s biomechanical performance. Wide-angle X-ray scattering was applied to seven healthy ex-vivo human eyes. Each eye was dissected into an anterior and a posterior cup, and radial incisions were used to flatten the tissue before microstructure characterisation. A method was developed to use the microstructure data obtained for the dissected tissue to build realistic 3D maps of fibril density and orientation covering the whole eye globe. At the central cornea, 61.5±2.3% of fibrils were aligned within 45° sectors surrounding the two orthogonal directions. In contrast, more than one-third of the total fibril content was concentrated along the circumferential direction at the limbus (37.0±2.4%) and around the optic nerve head (34.8±2.1%). The insertion locations of the four recti muscles exhibited a preference in the meridional direction near the equator (38.6±3.9%). There was also a significant difference in fibril density between the limbus and other regions (ratio = 1.91±0.45, p <0.01 at the central cornea and ratio = 0.80±0.21, p <0.01 at the posterior pole). Characterisation of collagen fibril density and orientation across the whole ocular surface has been possible but required the use of a technique that involved tissue dissection and hence caused tissue damage. The method presented in this paper aimed to minimise the effect of dissection on the quality of obtained data and was successful in identifying fibril distribution trends that were compatible with earlier studies, which concentrated on localised areas of the ocular globe.

Stress–Strain Index Map: A New Way to Represent Corneal Material Stiffness

“…Second, there is a strong consistency in microstructure distribution in healthy corneas with little variation between individuals. In an earlier study ( Zhou et al, 2019 ), in which comparisons were held between the microstructure maps of six healthy corneas, the standard deviations of collagen fibril contents (in the central 6 mm-diameter area) within the 45° sectors surrounding the superior–inferior and the temporal–nasal directions were 2.8 and 2.9%, respectively. Further, the corresponding standard deviation in the content of circumferential fibrils at 11 mm diameter was limited to 1.8%.…”

“…The SSI maps rely on the microstructure of corneal tissue, and in particular the distribution of collagen fibrils ( Zhou et al, 2019 ). Assuming that the SSI regional variation follows the distribution of collagen fibrils is based on evidence establishing collagen fibrils as the main load-carrying components of corneal tissue, and hence being responsible for corneal stiffness ( Daxer et al, 1998 ; Bell et al, 2018 ).…”

“…Assuming that the SSI regional variation follows the distribution of collagen fibrils is based on evidence establishing collagen fibrils as the main load-carrying components of corneal tissue, and hence being responsible for corneal stiffness ( Daxer et al, 1998 ; Bell et al, 2018 ). Relying on the link between microstructure and stiffness distribution was possible for five reasons; first, there is a considerable number of microstructure maps available for both healthy and keratoconic corneas ( Boote et al, 2006 ; Meek and Boote, 2009 ; Niederer and McGhee, 2010 ; Studer et al, 2010 ; Pijanka et al, 2013 ; Ho et al, 2014 ; Pandolfi et al, 2019 ; Zhou et al, 2019 ; Zvietcovich et al, 2019 ; Li et al, 2020 ; Rodriguez-Garcia et al, 2020 ). Second, there is a strong consistency in microstructure distribution in healthy corneas with little variation between individuals.…”

Numerical Simulation of Corneal Fibril Reorientation in Response to External Loading

“…While 256 fibril density measurements provided only 128 unique values, this amount of data at each scanned point presented a challenge in the analysis of reorientation. In earlier work, we conducted an optimisation study to determine the minimum number of orientations that could be adopted without significantly affecting the outcomes of numerical models based on this microstructure data [31]. In that work, 16 orientations were selected as sufficiently representative of the microstructure data and leading to a negligible effect on numerical model results below 0.08%.…”

“…As explained in our earlier publication, the regional variation and anisotropy of fibril distribution across the ocular globe were introduced in the material constitutive model through fitting the microstructure data to Zernike polynomials. The polynomials were then used to estimate the fibril density and angular distribution at the integration points of the model’s finite elements [10,31], Figure 1. In this method, the fibril distribution function K stored the fibril density data as illustrated in Equation (4).…”